Evaluation of Direct Collocation Optimal Control Problem Formulations for Solving the Muscle Redundancy Problem.
Evaluation of Direct Collocation Optimal Control Problem Formulations for Solving the Muscle Redundancy Problem.
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DOI：
10.1007/s10439-016-1591-9
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发表时间：
2016-10
影响因子：
3.8
通讯作者：
Fregly BJ
中科院分区：
文献类型：
--
作者：
De Groote F;Kinney AL;Rao AV;Fregly BJ
估计运动中的肌肉力涉及到解决一个不确定的问题(比关节力矩约束更多的未知肌力)，通常是通过优化方法。当肌肉激活和收缩的动力学被建模为与肌肉生理学一致时，所产生的优化问题是动态的，并且具有挑战性。这项研究试图找出一个稳健的和计算效率高的公式来解决这些动态优化问题，使用直接配置最优控制方法。基于二维和三维模型，研究了步行的四个问题公式。公式的不同之处在于，使用显式或隐式的收缩动力学表示，将肌肉长度或肌腱力作为状态变量。隐式表示引入了定义为状态的时间导数的附加控制，允许将描述收缩动力学的非线性方程强加为代数路径约束，从而简化了它们的求值。问题表述影响了计算速度和对初始猜测的稳健性。使用以肌肉长度为状态的显式收缩动力学的公式在大多数情况下无法收敛。相反，使用隐式收缩动力学的两个公式在所有初始猜测的所有情况下都收敛到最优解，作为一种状态的肌腱力通常是最快的。未来的工作应该侧重于将目前的方法与其他计算肌肉力量的方法进行比较。目前的方法缺乏一些已有方法的主要局限性，如静态优化和计算肌肉控制，同时保持计算效率。本文的在线版本(doi：10.1007/s10439-0161591-9)包含补充材料，授权用户可以使用。
Estimation of muscle forces during motion involves solving an indeterminate problem (more unknown muscle forces than joint moment constraints), frequently via optimization methods. When the dynamics of muscle activation and contraction are modeled for consistency with muscle physiology, the resulting optimization problem is dynamic and challenging to solve. This study sought to identify a robust and computationally efficient formulation for solving these dynamic optimization problems using direct collocation optimal control methods. Four problem formulations were investigated for walking based on both a two and three dimensional model. Formulations differed in the use of either an explicit or implicit representation of contraction dynamics with either muscle length or tendon force as a state variable. The implicit representations introduced additional controls defined as the time derivatives of the states, allowing the nonlinear equations describing contraction dynamics to be imposed as algebraic path constraints, simplifying their evaluation. Problem formulation affected computational speed and robustness to the initial guess. The formulation that used explicit contraction dynamics with muscle length as a state failed to converge in most cases. In contrast, the two formulations that used implicit contraction dynamics converged to an optimal solution in all cases for all initial guesses, with tendon force as a state generally being the fastest. Future work should focus on comparing the present approach to other approaches for computing muscle forces. The present approach lacks some of the major limitations of established methods such as static optimization and computed muscle control while remaining computationally efficient. The online version of this article (doi:10.1007/s10439-016-1591-9 contains supplementary material, which is available to authorized users.
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DOI：
10.1115/1.1531112
发表时间：
2003-02-01
影响因子：
1.7
作者：
Thelen, DG
通讯作者：
Thelen, DG
影响因子：
2.7
作者：
Patterson, Michael A.;Rao, Anil V.
通讯作者：
Rao, Anil V.
影响因子：
2.4
作者：
Steele, Katherine M.;Seth, Ajay;Delp, Scott L.
通讯作者：
Delp, Scott L.
影响因子：
2.2
作者：
Garg, Divya;Patterson, Michael A.;Rao, Anil V.
通讯作者：
Rao, Anil V.
影响因子：
1.5
作者：
Knarr, Brian A.;Reisman, Darcy S.;Higginson, Jill S.
通讯作者：
Higginson, Jill S.